Typically, the electronic properties of solids are portrayed using the band model [59]. When a solid is formed, isolated atom combine creating new molecular orbitals. The conduction band (CB) is formed of vacant antibonding orbitals, while the valence band (VB) is formed of filled orbitals. The electrical properties of the materials are controlled by the separation between these two bands, known as bandgap and characterised by the bandgap energy.The generation of bands in solids from atomic orbitals of isolated atoms is depicted in Figure 3.9
Figure 3.9Generation of bands in solids from atomic orbitals of isolated atoms [59].
For a good conductor the empty and filled energy levels coexist typically at the same energy level. This is the reason why only a very small activation energy needs to be used so that the electrons can be transferred from one level to another.
A model of the structure of the double layer at the metal/solution interface is presented in Figure 3.10. The solution side of the double layer is believed to be formed of a number of layers. The layer closest to the electrode, called the inner Helmholtz layer or plane (IHP), is formed of solvent molecules and other species specifically absorbed (unsolvated). The centre of the electrical charge is at a distance x1, while solvated ions can approach the electrode only to a distance x2. The centre of this charge is called the outer Helmholtz plane (OHP). The interactions of the ions with the electrode are independent of their chemical properties, involving only long range electrostatic forces. Due to the thermal agitation, these ions (solvated and unsolvated) are dispersed across in a three-dimensional region named the diffuse layer, which extends from the OHP into the bulk of the solution. The thickness of the
diffuse layer depends on the concentration of ions in solution and its structure can affect the rates of the electrode processes [60].
Figure 3.10Double layer region at the metal- electrolyte interface IHP, inner Helmholtz plane; OHP, outer Helmholtz plane [60].
In the case of intrinsic diamond, the 5.5 eV bandgap ensures that the valence band (VB) is almost completely filled up, while the conduction band (CB) is almost vacant at room temperature. The thermal excitation of electrons from the VB to the conduction band makes conduction in solids possible by creating electrons in the CB and holes in the valence band with a specific electrical mobility. Intrinsic semiconductors are typically characterised by this behaviour (see Figure 3.11).
Figure 3.11Energy bands of an intrinsic semiconductor.
Doping a diamond with boron (> 1017 cm-3), transforms the material from an insulator to a semiconductor (see Chapter 2, section 2.2). Because boron has a deficiency of electrons in its outer shell (compared to carbon) it will act as an acceptor. An energy level, EA, is introduced just above the valence band. Through thermal excitation the electrons move from the valence band into these acceptor sites. This behaviour confers diamond p-type semiconductivity as a result of the free electrons in the acceptor site and mobile holes in the valence band (Figure 3.12) [61]. For higher boron doping levels (1019- 1020 atoms cm-3) a mutual interaction between the boron centres forces the impurity band to broaden and shift towards the valence band and the diamond becomes metallic.
At the interface between a semiconductor electrode and any kind of electrolyte solution, if their potentials are not situated at the same level, an exchange of charge between the solution and the semiconductor will be necessary so that equilibrium can be reached. In the case of a metallic electrode, the charges are located just below the surface, but semiconductors behave differently. For semiconductors, since the carrier density is much smaller than in a metal electrode, the charges can be distributed on a significant distance, 100- 10000 Å, below the interface. A space charge layer is formed, similar to that in pure solid devices [59]. So, for semiconductor electrochemistry, the interfaces of interest are the electrode/electrolyte double layer and the space charge double layer.
The redox potential is higher than the level of the Fermi layer for a p-type semiconductor, and hence electron transfer must occur from the solution to the electrode to attain equilibrium. This generates a negative charge in the space charge region, which causes a downward bending in the band edges. Since the holes in the space charge region are removed by this process, this region is a depletion layer.
In a similar manner to metallic electrodes, modifying the potential applied to the semiconductor electrode changes the position of the Fermi level. The band edges in the interior of the semiconductor (i.e.away from the depletion region) also vary with the applied potential in the same way as the Fermi level. Nevertheless, the energies of the band edges at the interface are not affected by changes in the applied potential. Therefore, the change in the energies of the band edges on going from the interior of the semiconductor to the interface, and hence the magnitude and direction of band bending, varies with the applied potential [60]. Figure 3.13 shows a schematic representation of an energy diagram for a semiconductor-electrolyte interface for a standard potential.
Figure 3.13Energy diagram for a semiconductor- electrolyte interface for a standard redox potential [59]
The situations that can appear are: a) Flatband potential (Efb)
The Fermi energy lies at the same energy as the redox potential of the electroactive species of interest.As there is no charge transfer, there is no band bending.
b) Depletion region
For p-type semiconductors, depletion occurs as the electrode potential is poised negative of the flatband potential.
c) Accumulation region
For p-type semiconductors, accumulation occurs at electrode potentials more positive than the flatband potential.
The charge transfer abilities of a semiconductor electrode depend on whether there is an accumulation layer or a depletion layer. If there is an accumulation layer, the behaviour of a semiconductor electrode is similar to that of a metallic electrode, since there is an excess of the majority charge carrier available for charge transfer. In contrast, if there is a depletion
layer, then there are few charge carriers available for charge transfer, and electron transfer reactions occur slowly, if at all.